In order to get the weather aplet to work. Click on the applet, then click on your weather provider site. You need to register there to get your API-key . Copy/paste it in the “weather provider” section of the applat menu and you are done

I am not using XFCE; however, would you be able to check in your terminal for xfce --help
There might be a command to restart your DE and/or WM. For example, it might contain the command --replace (just an example)

Secondly, is there an option to replace your weather service provider. If there is, then it may prove better as the No Data could turn to data available. I have had this in the past myself and I wound up changing the weather service providers for the exact same problem.

Also, is there a navigation on your XFCE panel for properties and then to enable a restart script?